All Karen Hendrickson wanted was the latest pocketbook from Gucci, the Sylvie, with a glittering gold chain down the front.

But she had to explain herself over and over to police officers who stopped and questioned her, and searched her shopping bags as she sought to cross Fifth Avenue in Manhattan. She was trying to reach the Gucci flagship store on the corner of 56th Street, but her shopping trip had an unusual impediment: Gucci is inside Trump Tower. Fifty-eight stories above is the penthouse of President-elect Donald J. Trump, who was engaged in the rocky business of selecting his administration.

“I had to be questioned by three different police officers just to get into this store,” said Ms. Hendrickson, 47, who was visiting from South Orange, N.J., the Sylvie at last in her hand. As she mused on Mr. Trump’s being garrisoned in his penthouse apartment, she wondered why he was not preparing in Washington. “This isn’t a Monday-Friday job,” she said. “This is a very serious job, and you need to spend time in the White House.”

“Go to work now!” she added, her frustration eclipsing the fact that the White House is occupied until the end of January.

They came from as far as England, Italy and Mexico and as close by as Harlem to rarefied turf on the Upper East Side, all to take a selfie with Trump Tower’s golden sign in the background. Below it was a snarl of barricades, armored police officers, lead-footed tourists and aggrieved New Yorkers trying to go about their business. Double-decker tour buses crawled along, inching past on an avenue narrowed at points to a single lane by the police, who also scanned from above in a booth atop a cherry-picker.

Tourists and passers-by were given the once-over by a phalanx of bomb-sniffing dogs prowling the sidewalks. At times, impromptu news conferences congealed on the sidewalk or beside the elevator bank inside the rose-colored lobby, as dignitaries and members of Mr. Trump’s transition team came and went.

“I will not tell you that Gucci and Tiffany are my central concerns in life, but I will say the traffic situation is a very real problem,” Mayor Bill de Blasio said as he stood at a lectern on the sidewalk in front of the building, speaking to reporters after leaving an hourlong meeting with Mr. Trump. Mr. de Blasio, a Democrat, said he expressed to Mr. Trump, a Republican, that New Yorkers were fearful of the ramifications of his policies.

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A crowd on Wednesday outside Trump Tower in Manhattan. Security was tightened as President-elect Donald J. Trump held meetings inside.CreditHilary Swift for The New York Times

Some pedestrians battled the hordes angling for a photograph at what is now a must-stop on their way to or from Times Square.

Inside the building, in a women’s restroom painted pink, Shaopei Lu, 32, a secretary visiting from Shanghai, touched up her makeup. She had come to see Trump Tower, and though she had wended her way between police officers to get in, she had not realized that its eponym was upstairs. “Trump is living in this building?” she asked. “Can I have a chance to meet him?”

Others came to bear witness. “On 9/11, I went down to the waterfront on the Jersey side to see it on the same day,” said Jeff Fox, 65, a retired writer. “Some people have said 9/11 was a disaster, but so was 11/9,” he added, referring to the day after Election Day, when Mr. Trump was declared the winner.

A group of high school students visiting from Pennsylvania gathered on a corner and spat at the building.

Trump Tower is a mass of black glass and steel not far from Central Park, but since last week it has become New York’s White House-in-waiting. While Mr. Trump is inside fielding phone calls from world leaders and conferring with his inner circle, the surrounding sidewalks have become a cacophonous plaza, luring out-of-town visitors, curious New Yorkers, angry protesters and a scrum of reporters craning their necks to spot a potential cabinet member entering or exiting.

“I so disagree with his policies,” said Pete Thacker-Davis, 24, who was on his honeymoon from Birmingham, England, with his husband, David, 31. The couple, both restaurant managers, leaned on a police barricade on Fifth Avenue for two hours trying to spot Mr. Trump. “So that I could stand here and say that I actually saw him,” Mr. Thacker-Davis said, “that I actually saw the Devil himself.”

For the most part it was a placid scene pocked by intermittent eruptions of invective against Mr. Trump. This being New York, where disaffection is a credo and celebrities, presidents or presidents-elect are not a big deal, the city seemed to carry on — albeit a little bit irked.

The high school students, from Fort Washington, Pa., vented their displeasure over Mr. Trump’s election by making obscene hand gestures toward the building. “I genuinely think he hates me, hates my family,” said Kian Jamasbi, a senior, whose parents are from Iran. “They are Muslim, so it makes the feeling worse.”

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Cindi Chapman, who is visiting from Maine, took a selfie across the street from Trump Tower on Wednesday. “Whether I like him or not, it’s historic,” Ms. Chapman said.CreditHilary Swift for The New York Times

Calvin Hunt, 55, a community activist from Harlem, spent much of Wednesday afternoon with his 9-year-old son, Cameron, whom he had pulled out of school for the day. He held signs in support of Mr. Trump and exclaimed that black people like himself should support the president-elect. He screamed intermittently at the crowd, some of whom fired back. “If a black guy says Trump is good, that should be enough!” he bellowed.

Beside him a young woman quietly raised a poster that said “Not my president.” Mr. Hunt loudly exclaimed his opposition. “Those children shouldn’t be out protesting,” he shouted. “They should be at home playing Yahtzee, or Monopoly!”

Nearby on Fifth Avenue, Teresa Fisher, a hospital worker who was in town from Staples, Minn., for a business conference, gazed up at the tower with bewilderment. “This is a little overwhelming,” she said. “We haven’t seen chaos quite like this back home.”

“Open to the public” is emblazoned in gold on the lobby entrance of the tower, and except for the addition of a new magnetometer to scan bags, it is still open to visitors and has no metal detector. On Wednesday, those not intimidated by the Kevlar-decked officers outside headed down golden escalators to the Trump boutique, where Trump colognes with names like Success and Empire were on sale next to “Make America Great Again” hats. Each time customers approached with a hat, the cashier asked if they were United States citizens, citing campaign donation rules.

In the subterranean food court, Secret Service agents took lunch breaks, eating dishes like “Trump’s Mother’s Meatloaf” beside a waterfall several stories high that pours down a pink marble wall. Serving the meatloaf at the Trump Cafe was a worker who declined to provide his name because he was not authorized to speak about his employer.

An immigrant from Mexico, he said he supported the man whose name was on the coffee being served and was not troubled by Mr. Trump’s vow to deport millions of undocumented immigrants. “I’m not a criminal; I pay the taxes,” he said, spooning chicken and brussels sprouts into a plastic tub. “The people he is talking about are the crooks.”

In the atrium that connects Trump Tower to an adjacent building, Charlie Singleton, 48, a visitor from London, ate a lunch of French fries with a fork. He chose the building for the comfortable seating, not for the man inside, up above, planning how to govern the nation. The rigmarole outside was silly, Mr. Singleton said, because the election was over.

“I’m enjoying my food,” he said. “I wish him the best.”

Noah Remnick contributed reporting.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Hunkering Down at His Tower, Grinding Fifth Avenue to a Halt. Order Reprints | Today’s Paper | Subscribe